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Factoring via Strong Lattice Reduction Algorithms

Authors:
Harald Ritter
Carsten Roessner
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URL: http://eprint.iacr.org/1997/008
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Abstract: We address to the problem to factor a large composite number by lattice reduction algorithms. Schnorr has shown that under a reasonable number theoretic assumptions this problem can be reduced to a simultaneous diophantine approximation problem. The latter in turn can be solved by finding sufficiently many l_1--short vectors in a suitably defined lattice. Using lattice basis reduction algorithms Schnorr and Euchner applied Schnorrs reduction technique to 40--bit long integers. Their implementation needed several hours to compute a 5% fraction of the solution, i.e., 6 out of 125 congruences which are necessary to factorize the composite. In this report we describe a more efficient implementation using stronger lattice basis reduction techniques incorporating ideas of Schnorr, Hoerner and Ritter. For 60--bit long integers our algorithm yields a complete factorization in less than 3 hours.
BibTeX
@misc{eprint-1997-11290,
  title={Factoring via Strong Lattice Reduction Algorithms},
  booktitle={IACR Eprint archive},
  keywords={},
  url={http://eprint.iacr.org/1997/008},
  note={Appeared in the THEORY OF CRYPTOGRAPHY LIBRARY and has been included in the ePrint Archive. roessner<at>cs.uni-frankfurt.de 10500 received June 13th, 1997.},
  author={Harald Ritter and Carsten Roessner},
  year=1997
}